It started when Jesus was an infant; Joseph and Mary took the infant Jesus by night into Egypt to flee from King Herod’s murderous plot to kill all the baby boys in Bethlehem. Later, God would call His Son “out of Egypt”, just as He called His Old Testament “son” – the nation of Israel – out of Egypt centuries before.
The connection to the Exodus is reinforced in the Transfiguration of Jesus. As Jesus is shining in heavenly glory – His face and clothes gleaming white as light and bright as the sun–Moses and Elijah appear with Him. The glorified Old Testament prophets stand with Jesus, and we are told they are talking about His “departure” – that word “departure” is the word exodus!
Even without knowing Greek, you can see the similarity of the English word “exodus” with the Greek word ἔξοδος in Luke 9:31! The English word is simply transliterated from the Greek–and both go back to the Old Testament “exodus” of the Israelites out of Egypt under Moses’ leadership. Read the fascinating account of the Israelites’ “salvation journey” to the promised Land in the Old Testament books of Exodus and Numbers!